Solve 0=x-1 / (x-3) (x+2)

x = 2 + sqrt (6) or x = 2 - sqrt (6)

Step-by-step explanation by completing the square:

Solve for x:

0 = x - (x + 2) / (x - 3)

0 = x - (x + 2) / (x - 3) is equivalent to x - (x + 2) / (x - 3) = 0:

x - (x + 2) / (x - 3) = 0

Bring x - (x + 2) / (x - 3) together using the common denominator x - 3:

(x^2 - 4 x - 2) / (x - 3) = 0

Multiply both sides by x - 3:

x^2 - 4 x - 2 = 0

Add 2 to both sides:

x^2 - 4 x = 2

Add 4 to both sides:

x^2 - 4 x + 4 = 6

Write the left hand side as a square:

(x - 2) ^2 = 6

Take the square root of both sides:

x - 2 = sqrt (6) or x - 2 = - sqrt (6)

Add 2 to both sides:

x = 2 + sqrt (6) or x - 2 = - sqrt (6)

Add 2 to both sides:

Answer: x = 2 + sqrt (6) or x = 2 - sqrt (6)